1. Technical Field
The invention relates generally to forecasting systems modeling credit risk. More particularly, the invention relates to a computer implemented method and apparatus for modeling default risk in view of incomplete information.
2. Description of the Prior Art
To a corporate bond investor, there is no piece of information more valuable than the likelihood that an issuer will default. Correspondingly, in the wake of the burgeoning corporate bond and credit derivative markets, there is a fast-growing industry that builds models to estimate default probabilities and tools to manage portfolios that contain credit-sensitive instruments. There are currently two main quantitative approaches to credit risk management.
The structural approach takes the cause and effect nature of default as a starting point and thereby relies on a precise definition of a default event. It should be appreciated that it can be difficult to give a precise definition of default that is of practical use to modelers and designers of credit derivatives. Working definitions include missed principal or interest payments, firm value falling below a specified boundary, and firm restructuring. Structural models were introduced in R. Merton, On the pricing of corporate debt: The risk structure of interest rates, Journal of Finance 29, 449-470, (1974). Merton's fundamental insight was that firm debt can be viewed as a portfolio of government bonds and a short put option on the firm value. Black and Cox (1976) extended these seminal contributions by allowing for a broader definition of default. For example, the bondholders may have the right to force liquidation as soon the firm value falls to some prescribed lower threshold. Thus, in the structural framework the value of the debt and the probability of default can be backed out of an appropriately calibrated option formula.
The Merton and Black and Cox models, as well as many other models, are compelling but have the unintended consequence of placing default in the realm of predictable events. By predictable, it is meant that the default event is foreshadowed by an observable phenomenon, such as the value of the firm falling dangerously close to its default boundary.
In reality default, or at least the moment at which default is publicly known to be inevitable, usually comes as a surprise. This is highlighted in the credit market by the prevalence of positive short-term credit spreads. If default were truly predictable, the term structure of credit spreads would decrease to zero with maturity. The prediction of zero short-term spreads is one of the difficulties with traditional structural models.
In contrast to the structural approach, the reduced form approach is based on the assumption that default is totally unpredictable; i.e. it hits the market by surprise. In a reduced form model, each firm comes equipped with an intensity, or conditional default arrival rate. The intensity λ(t,ω)is a function of time t and state of the world ω. It is the instantaneous rate of default, given that a firm escapes default until time t and is in state ω. It is straightforward to calculate probability of default from the intensity. Further, the intensity is one of the main ingredients in the calculation of prices of default securities. Because of the embedded assumption that default is totally unpredictable, reduced form models can be calibrated to the short positive spreads that are pervasive in the market.
From a modeling perspective, it seems very natural to integrate both approaches, so as to retain both the economic appeal of the structural approach and the empirical plausibility as well as the tractability of the intensity-based approach. However, to integrate both approaches is very difficult because of conflicting assumptions underlying the better known structural models and reduced form models. Thus, the most basic structural/reduced form hybrid models are fundamentally flawed.
It should be appreciated that for the purpose of measuring default risk, neither approach explicitly accounts for the fact that investors rely on information that is imperfect. It would therefore be advantageous to provide a framework directly addressing this issue.
It would further be advantageous to provide a computer implemented method and apparatus that provides a hybrid default model that incorporates the best features of both traditional structure and reduced form approaches while avoiding their shortcomings and such that the assumptions underlying the component models are compatible.